On operators from $\ell_{s}$ to $\ell_{p}\widehat{\otimes}\ell_{q}$ or to $\ell_{p}\widehat{\widehat{\otimes}}\ell_{q}$

Volume 121 / 2010

Christian Samuel Colloquium Mathematicum 121 (2010), 25-33 MSC: Primary 46B28; Secondary 47L20. DOI: 10.4064/cm121-1-3

Abstract

We show that every operator from $\ell_{s}$ to $\ell_{p}\mathbin{\widehat{\otimes}}\ell_{q}$ is compact when $1\leq p,q< s$ and that every operator from $\ell_{s}$ to $\ell_{p}\mathbin{\widehat{\widehat{\otimes}}}\ell_{q}$ is compact when $ 1/p+1/q>1+1/s. $

Authors

  • Christian SamuelLATP Laboratoire Analyse, Topologie, Probabilités
    Faculté des Sciences et Techniques
    Université Aix-Marseille 3
    13397 Marseille Cedex 20, France
    e-mail

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